This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A188737 #11 Sep 08 2022 08:45:56 %S A188737 2,7,0,3,2,5,7,4,0,9,5,4,8,8,1,4,5,5,1,6,6,7,0,4,5,7,1,3,6,2,7,1,3,2, %T A188737 1,9,2,8,7,4,4,6,7,5,0,8,1,2,0,4,1,0,6,6,8,0,0,1,2,9,2,0,3,4,2,4,0,4, %U A188737 4,5,1,7,1,1,3,3,6,4,5,9,1,0,1,2,7,9,8,2,3,4,8,4,6,5,5,4,6,7,6,0,8,2,3,3,8,9,9,6,8,1,4,6,4,7,8,6,1,4,0,2,5,3,5,4,1,1,0,5,5,7 %N A188737 Decimal expansion of (7+sqrt(85))/6. %C A188737 Decimal expansion of the length/width ratio of a (7/3)-extension rectangle. See A188640 for definitions of shape and r-extension rectangle. %C A188737 A (7/3)-extension rectangle matches the continued fraction [2,1,2,2,1,2,2,1,2,2,1,...] for the shape L/W=(7+sqrt(85))/6. This is analogous to the matching of a golden rectangle to the continued fraction [1,1,1,1,1,1,1,1,...]. Specifically, for the (7/3)-extension rectangle, 2 squares are removed first, then 1 square, then 2 squares, then 2 squares,..., so that the original rectangle of shape (7+sqrt(85))/6 is partitioned into an infinite collection of squares. %H A188737 G. C. Greubel, <a href="/A188737/b188737.txt">Table of n, a(n) for n = 1..10000</a> %e A188737 2.703257409548814551667045713627132192874467508120... %p A188737 evalf((7+sqrt(85))/6,140); # _Muniru A Asiru_, Nov 01 2018 %t A188737 r = 7/3; t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t] %t A188737 N[t, 130] %t A188737 RealDigits[N[t, 130]][[1]] %t A188737 ContinuedFraction[t, 120] %o A188737 (PARI) default(realprecision, 100); (7+sqrt(85))/6 \\ _G. C. Greubel_, Nov 01 2018 %o A188737 (Magma) SetDefaultRealField(RealField(100)); (7+Sqrt(85))/6; // _G. C. Greubel_, Nov 01 2018 %Y A188737 Cf. A188640. %K A188737 nonn,cons %O A188737 1,1 %A A188737 _Clark Kimberling_, Apr 12 2011